The application of optical processing systems to security, verification, and encryption of information has been explored previously (H.-Y. Li, Y. Qiao, and D. Psaltis, “Optical Network For Real-time Face Recognition,” Appl. Opt. 32, 5026–5035 (1993); B. Javidi and J. L. Horner, “Optical Pattern Recognition For Validation and Security Verification,” Opt. Eng. 33, 1752–1756 (1994); Ph. Refrégier and B. Javidi, “Optical Image Encryption Based on Input Plane and Fourier Plane Random Encoding,” Opt. Lett. 20, 767–769 (1995); C. L. Wilson, C. I. Watson, and E. G. Paek, “Combined Optical and Neural Network Fingerprint Matching,” Proc. SPIE 3073, 373–382 (1997); N. Yoshikawa, M. Itoh, and T. Yatagai, “Binary Computer-generated Holograms for Security Applications From A Synthetic Double-exposure Method by Electron-beam Lithography,” Opt. Lett. 23, 1483–1485 (1998) and O. Matoba and B. Javidi, “Encrypted Optical Memory System Using Three-dimensional Keys in the Fresnel Domain,” Opt. Lett. 24, 762–764 (1999); which are incorporated herein by reference).
In one approach, the information to be secured or verified is encoded as a two-dimensional image using amplitude, phase, polarization or wavelength modulation of light and optically processed. In order to encrypt the information, random phase-codes can be used to modify the Fraunhofer or Fresnel diffraction patterns of the input image (B. Javidi and J. L. Horner, “Optical Pattern Recognition For Validation and Security Verification,” Opt. Eng. 33, 1752–1756 (1994); Ph. Refrégier and B. Javidi, “Optical Image Encryption Based on Input Plane and Fourier Plane Random Encoding,” Opt. Lett. 20, 767–769 (1995) and O. Matoba and B. Javidi, “Encrypted Optical Memory System Using Three-dimensional Keys in the Fresnel Domain,” Opt. Lett. 24, 762–764 (1999)) as in methods for securing or multiplexing holographic memories (J. E. Ford, Y. Fainman, and S. H. Lee, “Array Interconnection By Phase-coded Optical Correlation,” Opt. Lett. 15, 1088–1 090 (1990); C. Denz, G. Pauliat, G. Roosen, and T. Tschudi, “Volume Hologram Multiplexing Using A Deterministic Phase Encoding Method,” Opt. Commun. 85, 171–176 (1991); H. Lee and S. K. Jin, “Experimental Study of Volume Holographic Interconnects Using Random Patterns,” Appl. Phys. Lett. 62, 2191–2193 (1993); J. F. Heanue, M. C. Bashaw, and L. Hesselink, “Encrypted Holographic Data Storage Based on Orthogonal-phase-code Multiplexing,” Appl. Opt. 34, 6012–6015 (1995); C. Denz, K. O. Mueller, F. Visinka, and T. I. Tschudi, “Digital Volume Holographic Data Storage Using Phase-coded Multiplexing,” Proc. SPIE. 3802,142–147 (1999) and C. C. Sun, W. C. Su, B. Wang, and Y. Ouyang, “Diffraction Selectivity of Holograms With Random Phase Encoding,” Opt. Commun. 175, 67–74 (2000) which are incorporated herein by reference).
In general, the encrypted image contains both amplitude and phase and thus holographic recording may also be required (J. W. Goodman, Introduction to Fourier Optics, McGraw-Hill, New York, 1996 which is incorporated herein by reference). This necessity makes it difficult to transmit the encrypted information over conventional communication channels.
Several digital holography methods have been applied to solve the previous problem by recording fully complex information with electronic cameras (U. Schnars and W. P. O. Juptner, “Direct Recording of Holograms By A CCD Target and Numerical Reconstruction,” Appl. Opt. 33, 179–18 1 (1994); Y. Takaki, H. Kawai, and H. Ohzu, “Hybrid Holographic Microscopy Free of Conjugate and Zero-order Images,” Appl. Opt. 38, 4990–4996 (1999) and E. Cuche, F. Bevilacqua, and C. Depeursinge, “Digital Holography For Quantitative Phase-contrast Imaging,” Opt. Lett. 24, 291–293 (1999) which are incorporated herein by reference). Among them, digital phase-shifting interferometry stands out as a versatile and efficient technique (J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, and D. J. Brangaccio, “Digital Wavefront Measuring Interferometer For Testing Optical Surfaces And Lenses,” Appl. Opt. 13, 2693–2703 (1974); J. Schwider, “Advanced Evaluation Techniques In Interferometry,” in: Progress in Optics, Vol. XXVIII, ed. E. Wolf, pp. 271–359 (North-Holland, Amsterdam, 1990) and I. Yamaguchi and T. Zhang, “Phase-shifting Digital Holography,” Opt. Lett. 22, 1268–1270 (1997) which are incorporated herein by reference).
A first attempt to electronically record the holographic information associated with a two-dimensional encrypted image has already been reported by using off-axis digital holography (B. Javidi and T. Nomura, “Securing Information By Means Of Digital Holography,” Opt. Lett. 25, 28–30 (2000) which is incorporated herein by reference) and inline digital holography (E. Tajahuerce, O. Matoba, S. C. Verrall, and B. Javidi, “Optoelectronic Information Encryption With Phase-shifting Interferometry”, Appl. Opt. 39, 23 13–2320 (2000) which is incorporated herein by reference). In this way, advantages of optical encryption such as speed, large number of degrees of freedom and high security, are combined with the usefulness of electronic information transmission.
Optical encryption and security are recent applications of optical information processing. (F, Goudail, F, Bollaro, B. Javidi, and Ph. Refregier, “Influence of A Perturbation In A Double Phase-encoding System,” J. Opt. Soc. Am. A 15, 2629–2638(1998); H. Y. Li, Qiao and D. Psaltis, “Optical Network For Real-time Face Recognition,” Appl. Opt. 32, 5026–5035 (1993); Ph. LaLanne, H, Richard, J. C. Rodier, P. Chavel, J. Taboury, K. Madani, P. Garda and F. Devos, “2D Generation of Random Numbers By Multimode Fiber Speckle for Silicon Arrays of Processing Elements,” Opt. Commun. 76, 387–394 (1990) and J. L. Horner and B. Javidi, eds., Optical Engineering Special Issue on Optical Security (SPIE, Belingham, Wash., 1999), Vol. 38, which are incorporated herein by reference). Optical systems present a good potential for these tasks because, they provide a large degree of freedom to secure data. Several different techniques exist to secure and store data by phase encoding. (T. F. Krile, M. O. Hagler, W. D. Redus and J. F. Walkup, “Multiplex Holography With Chirp-modulated Binary Phase-coded Reference-beam Masks,” Appl. Opt. 18, 52–56 (1979) and Y. H. Kang, K. H. Kim and B. Lee “Volume Hologram Scheme Using Optical Fiber for Spatial Multiplexing,” Opt. Lett. 22, 739–741 (1997) which are incorporated herein by reference) In each case the encrypted data are fully complex and thus may be recorded and stored holographically. (H. J. Caulfield, ed., Handbook of Optical Holography (Academic, London, 1979) which is incorporated herein by reference). A high quality reconstruction can be obtained by use of a high density analog recording medium. However, information recorded in this way is difficult to transmit over digital communication lines. If not digitized, or converted in some way, this information must be reconstructed optically.
One way in which fully complex information may be stored or communicated digitally is to record it with digital holography. (L. Onural and P. D. Scott, “Digital Decoding of In-line Holograms,” Opt. Eng. 26, 1124–1132 (1987); U. Schnarrs, “Direct Phase Determination In Hologram Interferometry With Use of Digitally Recorded Holograms,” J. Opt. Soc. Am. A 11, 2011–2015 (1994); G. Pedrini, Y. L. Zou and H. J. Tiziani, “Digital Double-pulsed Holographic Interferometry for Vibration Analysis,” J. Mod. Opt. 40, 367–374 (1995); J. C. Marron and K. S. Schroeder, “Three-dimensional Lensless Imaging Using Laser Frequency Diversity,” Appl. Opt. 31, 255–262 (1992); U. Schnarrs, T. M. Kreis and W. P. O. Juptner, “Digital Recording and Numerical Reconstruction of Holograms: Reduction of the Spatial Frequency Spectrum,” Opt. Eng. 35, 977–982 (1996) and E. Cuche, F. Bevilaqua and C. Depeursinge, “Digital Holography for Quantitative Phase-contrast Imaging,” Opt. Lett. 24, 291–293 (1993) which are incorporated herein by reference). With this method holograms are captured by an electronic camera and reconstructed by use of a digital computer that approximates a diffraction integral. These digital holograms may also be reconstructed optically, but digital reconstruction allows the focus to be adjusted electronically.
A method for using the CCD capabilities more efficiently is by digital phase-shifting interferometry to record the fully complex information. (K. Creath, “Phase-measurement Interferometry Techniques,” in Progress In Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1990), Vol. XXVI, pp. 349–393 and T. Zhang and I. Yamaguchi, “Three-dimensional Microscopy With Phase-shifting Digital Holography,” Opt. Lett. 23, 1221–1223 (1998) which are incorporated herein by reference). This phase-measurement technique is more precise than that of digitally recording an off-axis hologram. Generally, the system errors decrease with an increase in the number of phase-shift steps used to infer the fully complex information. However, it should be noted that, with currently available technology, the largest sources of system errors are the limited resolution and dynamic range of commercially available CCD arrays.